A new way of analyzing tooth movement using universal coordinate system geometry single point superposition in a 3D model

ABSTRACT Introduction: Superposing 3D models is an imminent need. However, current methods rely on marking multiple points on the maxilla and mandible, which could increase point marking and overlapping errors. Objective: This study aimed at developing a method for superimposing 3D models of the maxillary and mandibular arches with Autodesk Inventor® engineering software, using a single universal coordinate system (UCS) point superposition. Methods: A total of 104 STL (stereolithography) models of the maxillary and mandibular arches exported from My iTero® platform were retrospectively selected, in which T0 and T1 were the initial and refinement periods, respectively (n=26 per group). The X, Y, and Z coordinates associated with a single point in each arch were inserted into the models with SlicerCMF® software for model orientation. The arch models with UCS registration were transferred to Autodesk Inventor® for superimposition and to measure tooth movements performed during Invisalign® treatment. Arch expansion, intrusion and rotation were analyzed by two examiners. The statistics were performed using intraclass correlation coefficients (ICC), Dahlberg’s formula, and t-test (p<0.05). Results: A reliable method of superimposing 3D digital models using a single UCS point in the maxilla and mandible was developed. ICC showed excellent intra- and inter-examiner correlation (ICC>0.90). A systematic error was not found concerning linear and angular measurements (<1mm and <1.5°, respectively). Digital dental movements could be analyzed, including arch expansion, dental intrusion, and tooth rotation. Conclusions: The developed method was proven reliable and reproducible for superimposing 3D models of the maxillary and mandibular arches by using UCS system.


INTRODUCTION
Digital model superimposition is mainly used for observation of occlusal changes caused by craniofacial growth, 1,2 analysis of accuracy and predictability of orthodontic treatment with aligners, 3,4 and evaluation of orthodontic tooth movement. [5][6][7][8] The use of three-dimensional (3D) digital models for orthodontic outcome analysis has advantages over other methods, such as less exposure to radiation, quality of image visualization and lower cost. 7 Several methods seek reliability for overlapping 3D models by demarcating points in the maxilla and mandible that are stable and do not move during orthodontic treatment. 6,[9][10][11] Studies that looked for superimposition points in the maxilla observed that the most stable is situated in the posterior part of the incisor papilla and the palatal rugae. 10,12,13 Regarding the mandible, solid points that can be used for superimposition in 3D models are scarce. 7,11 Thus, there is a need for studies to establish a stable point for better accuracy in mandibular superimposition. 14 Dental software programs have been developed to assist orthodontists in treatment planning, but all have shown limitations and difficulties when used in research. [15][16][17] Autodesk Inventor ® is an engineering software program that uses the Computer-Aided Design/Computer-Aided Manufacturing (CAD/CAM) system to build products and items, and to help understand how a product or body behaves under certain conditions. It uses the Universal Coordinate System (UCS) that defines the orientation of the Cartesian axes X, Y, and Z in three-dimensional space, associated with a single point mark on the part/model with high accuracy. Autodesk Inventor ® was used to evaluate implant accuracy. 18 Due to its advantages, the use of Autodesk Inventor ® in the superimposition of 3D models in Dentistry might bring reliability and agility to the studies of three-dimensional movements in the maxillary and mandibular arches. 18 Understanding the step-by-step of superposition is mandatory for analyzing 3D models. 19 However, it is known that this is not simple and that the researcher or clinician can face many difficulties. In this sense, to overcome these obstacles and make 3D analyses simpler, more effective and cheaper, this study aimed to provide a step-by-step protocol of 3D models superimposition of the maxillary and mandibular arches, by marking a single point using the UCS geometry with SlicerCMF ® and Autodesk Inventor ® software. Align Technology, Santa Clara, CA, USA) (Fig 1). One participant carried out a restorative treatment and lost the follow-up in the refinement phase, thus a total of 26 participants were included in the study (Fig 1).

MATERIAL AND METHODS
The maxillary and mandibular arches were scanned using an iTero ® scanner (model Element, S/N: RTC2018 W06A228) by two operators, under the same conditions, at two time-points: T0 (start of treatment) and T1 (refinement phase). Models superimposition and analysis were performed using SlicerCMF ® (version 4.11; http://slicer.org) and Autodesk Inventor ® software. The first step was to determine the maxillary or mandibular landmarks in the 3D SlicerCMF ® software, to generate the UCS coordinate system numbers in T0 and T1 models. In the maxilla, the reference point was created with a vertical line passing through the medial region of the palate suture and a horizontal line passing through the upper region of the second palate rugae. The intersection between these lines was considered the region of interest and a landmark was created (Fig 2).
To standardize the superposition process in the mandible, a vertical line passing through the midline region was developed with a horizontal line passing through the mucogingival junction (Fig 2). The intersection between these lines was considered the region of interest and a landmark was developed.
The X, Y, and Z coordinates were then set from these maxillary and mandibular landmarks, establishing stable references in space in T0 and T1 models. Afterward, the X, Y, and Z coordinates were copied and used in Autodesk Inventor ® (Fig 3) to promote an overlap between the geometric points in T0 and T1 models. After superimposing models, tooth movement was Figure 3: Flowchart indicating a summary of the stepby-step procedure for marking points on the maxilla and mandible using Slicer 3D ® software and superimposing models in Autodesk Inventor ® software. measured in Autodesk Inventor ® (Fig 4). The 3D movements of buccolingual translation of maxillary and mandibular canines, premolars and molars were analyzed, and the intrusion and rotation movements of the mandibular incisors and canines were measured. The intra-and inter-examiner calibration was performed. Examiner 1 (RS) repeated the measurements twice with a 15-day interval (intra-examiner) and Examiner 2 (JP) performed these measurements once (inter-examiner). A detailed description of the methodology was prepared and can be seen in the supplementary material (Suppl. Table 3).

STATISTICAL ANALYSIS
The results were expressed as mean ± standard deviation. Intraand inter-examiner agreements were calculated using an intraclass correlation coefficient (2-way random, single measurement, absolute agreement) and Bland-Altman plot, 1  The study generated a step-by-step guide that can be accessed in the supplementary material (Suppl.  The amount of vertical movement was observed in the Z-axis in millimeters (Suppl. Table 3 and Fig. 5). The " Step-by-step" video can be watched through the QR code above ( Fig 5).

INTER-AND INTRA-EXAMINER MEASURES SHOWED A HIGH DEGREE OF AGREEMENT
Intra-and inter-examiner measures showed a high degree of agreement, analyzed by ICC and Bland-Altman statistical tests, indicating that the methodology of 3D models superposition was effective (Tables 1 and 2).      In the linear and rotation measures, Dahlberg values were always smaller than 1 mm and smaller than 1.5°, respectively, demonstrating that no systematic error was found for intra-and inter-examiners (Tables 1 and 2). it. 8,12,19,[22][23][24] The search for stable structures that are not influenced by orthodontic movement has been the main prerogative of current studies. 7 Even in cases of orthodontic aligners, in which no movement of posterior teeth is planned, making them supposedly immobile, tooth movement is observed. 3 In this study, we standardized a method to establish landmark points on the maxilla and mandible, to reduce this identification error.
In the present method, the points were created by the inter- Cartesian axes (X, Y, and Z) were generated and the software aligned these axes in T0 and T1 models, creating infinite points of spatial superposition with stability and reproducibility, as it is a stable and accessible structure present in all cases. 1,7,19,24 In the maxilla, studies have shown that the rugae regions, especially the second and third rugae, are stable regions for superimposition. 1,11,24,25 In the current study, the Cartesian axes with a single point in the medial region of the second rugae was used for superimposition of the maxillary models. This area is considered safe because it is not affected by tooth movement, 8,10,19 thus decreasing the chance of errors during similar points marking.
Several studies seek to increase the reliability of superposition by searching for spatial reference planes using manual tools for the elaboration of the coordinates. 6,11,12,16,19,27 The use of only one point in each 3D model was possible due to the use of the Autodesk Inventor ® is commonly used in bioengineering for stress and strain assessment, which requires accurate positioning of the models before mechanical analyses. 28,29 In the present research, this software was fundamental to ensure the correct positioning of the models, which is essential in studies for 3D models superimposition. Autodesk Inventor ® , as well as other CAD/CAM software, is compatible with several 2D and 3D file extensions, especially the so-called "neutral formats", such as Standard Triangle Language (STL), and Parasolid (x_t). 24 The use of this software proved to be very useful in this study, since the maxilla and mandible scans performed in Invisalign ® orthodontic treatments use the STL format. Thus, it was possible to easily manipulate the models using Autodesk Inventor ® 2D and 3D design tools. The software used in our research was the freely available SlicerCMF ® , which is commonly used in Dentistry and has demonstrated its accuracy and reliability. 19 It has been used for superimposing 3D models of the maxilla, despite using several points on the palatal rugae, 19,30 and for superimposing points on the mucogingival region of the mandible, using 13 points as a reference for superimposition. 1,19 Herein, we used the SlicerCMF ® for single point demarcation on both T0 and T1 models. The superimposition was not performed by this software as it requires more than one point for this purpose. 19 In this study, the points in the lingual mucosa gingival region were easily visualized and demarcated, and registered through the association with the X, Y, and Z coordinates generated by the software itself.
In the present research, the treatment was focused on mild The STL models were obtained retrospectively by scanning exclusively with iTero ® , as carried out in other studies, [31][32][33] and the spatial position of the models was established by this program automatically. Our focus was to standardize the methodology by choosing cases treated with the same align system, as well as using STL files obtained from the same scanner brand and handled by two operators. We believe that these precautions make the standardization of the methodology more effective. In future studies, another scanner brand may be used to evaluate if this is a factor that influences the spatial positioning of the models.
Regarding the limitation of the current study, we need to point out that superposing models and measuring tooth movement was not possible in cases in which restorative or periodontal procedures were performed during the orthodontic treatment. A total of 27 participants were selected for the study.
One patient was lost to follow-up and discontinued evaluation due to carrying out restorative treatment in T1; so the study was carried out with the remaining 26 participants who had agreed to participate. Another important point is the non-comparison between our method and others in the literature, to assess the accuracy of our systematization. Our main objective was to describe this accessible method that has proven to be effective for superimposing models, and it will be necessary to analyze the accuracy and predictability of this new method as compared with others. 1,19 Thus, further studies are needed to determine the level of accuracy of the methodology. Inexperience with engineering software can become a real challenge and limitation for dental researchers. However, in this study a very detailed step-by-step procedure was developed explaining complex and unfamiliar commands, which may become easy and intuitive after professional training. After the high agreement and reproducibility results achieved with this program, it may become a new and useful diagnostic tool for outcome assessment and orthodontic treatment predictability within all clinicians' reach.

CONCLUSIONS
We can conclude that an effective method for superimposing 3D models using UCS geometry was created, using the 3D SlicerCMF ® and Autodesk Inventor ® free softwares. This model was effective in promoting the superposition of the maxillary and mandibular models and in measuring tooth movements, such as tooth expansion, rotation, intrusion, and extrusion.  Table 1. Sample size calculation. The sample size calculation for comparative 2 studies that involve the comparison of two groups (inter-or intra examiner) was performed to 3 verify the number of patients to be used in the research. To determine the value of N an 4 equation comparing two means was used, as previously described by Eng (2003) 1 . Thus, the 5 formula for calculating the sample size for a reliable estimate of the population mean is given 6 bellow.  Table), as they were one of the most unstable biological variables found in this study. The standard deviation found for the A-P in the right canine was 1.39; while the difference between the means of A-P measurements from the right canine and the right first premolar was 0.4489  Table 2. Inclusion and exclusion criteria and inter-e intra-examiner's calibration Inclusion criteria: patients who had Class I, II and III malocclusion with moderate inferior crowding of up to 4 mm, change in overbite (from 3 to -5 mm), permanent dentition, presence of all teeth up to the second molars, aged 18 to 45 years.
Exclusion criteria: patients who had restorations in the teeth moved during treatment, non-cooperating patients with craniofacial syndromes or anomalies, and those with signs or symptoms of inflammation in the periodontal tissues. Three cases were discarded, two because the mesh was distorted for unknown reasons and one because a composite resin restoration was inserted in a tooth after movement altering the dental proportion, resulting 11 pairs of STL models. All participants were treated by the same professional in a private clinic in Belo Horizonte, Minas Gerais, Brazil and the cases were selected retrospectively.

Inter e intra examiner's calibration:
To evaluate the calibration of the main examiner (RS) with the software, a total of 22 measurements were taken, after superimposition 10 on posterior teeth in the bucco-lingual direction of canines, first and second premolars, first and second molars mandibular and maxillary represented by the X axis, in millimeters; 6 measurements in the vertical direction on anterior teeth of canines and mandibular incisors, movement represented by the Z axis in millimeters; and, 6 measurements on anterior teeth for the mesio-distal rotation, carried out by mandibular and maxillary incisors and canines, analyzed in degrees. The superimposition of 11 STL models were performed, totaling 242 measurements in 286 teeth, in both phases T0 (initial) and T1 (refinement), and repeated 2 times with a 15-day interval between them. To evaluate the accuracy and reliability, the same measurements were repeated by two examiners (RS-and GS) of the 11 cases. The two examiners did not participate in the orthodontic treatment. Choose File ( red arrow) to upload STL model and then in "choose a file to add" (second picture red arrow).

Supplemental
Step by step process to choose mandibular and maxillary superimposition points using UCS working geometry in initial and final STL models. Select STL models and click on: "OK". Both, initial and final, will appear on the screen.
Select one of the models to change it's color. It will make it easier to analyze. Click on "Welcome to Sliced (red arrow), and select "data" (yellow arrow). Click on "welcome to slicer"( red arrow) and select " data"( yellow arrow).
Both, initial and final, will appear on the screen.

Identify initial and final models
First click on "data,"(red arrow), then on IGT (yellow arrows) and finally on Fiducial Registration Wizard (green arrow). We are going to identify the models by changing their name First click "none"(red arrow) and then on "Create new markups fiducial as" (yellow arrow) to change models identification. Repeat the process with the other STL model.

Marking the maxilar or mandibular point is on each model
To make it easier, you can remove the visibility of one of the models by clicking on the icon ( red arrow).

Mandibular landmarck
To select a landmark press "Place markup point"(red arrow). Then, position the cursor at the intersection point between the dental and papillary midline and the mucogingival line (red circle).

Universal Coordinate System
The program will generate a UCS coordinate( red arrow) that will be used to overlay models the Autodesk program. Repeat the process with T1 model. In the second picture we can observe T0 and T1 models with the marked superimposition points.

Save landmark position and copy UCS coordinates
Red arrows indicate the process to save landmark positioning information. After saving information you will need to copy and paste USC coordinates ( red rectangle) to use this information in Autodesk software. Then, click on "Import Units" , select the measurement unit "millimeter" (red arrow). After that, click on the "ok" button (yellow arrow).
To finish this process click on "open" (red arrow).

Continue the calibration process in Autodesk software
Then, click on "tools"( black arrow) and after on "application options (red arrow).
After that click on "file" (black arrow) and on "configure default template" (red arrow). Set "millimeters" as the unit of interest (second picture black arrow) and then click on "ok"( second picture red arrow).

Visualize STL model
To better visualize teeth and arch morphology please click on "view" (red arrow), "view style" (yellow arrow) and then " realistic" (blue arrow).

Insert USC coordinates
Click on " 3D model"( red arrow) and then on "UCS" (yellow arrow). Copy the coordinates ( one by one ) in the following order: X,Y Z. When you are finished click on "enter" twice and save T0 model. Insert negative sign if necessary. Repeat the same process with T1 model.

Save T0 and T1 models with UCS coordinates
Save files to superposition process. Click on " file"(red arrow),"save"(blue arrow) and " save"( yellow arrow). Identify T0 and T1 models.

Superposition of 3D T0 and T1 models
To start superposition go to "File" (red arrow), "new"( yellow arrow) and "assemble"(blue arrow. Then click on "place"( red arrow in the second pict and "place" (yellow arrow second picture).

Models will open with UCS coordenate vectors
Both, T0 and T1 3D models will open (red arrow). Observe that UCS coordinates will apear (blue, greed and red vectors in initial and final models). Change the color of the initial model to simplify visualization. Click on the model ( second picture red arrow) and "adjust" (yellow arrow).

Change initial models color to better visualize superposition
Modify color using color cursor (red arrow) and then confirm the color you want to change ( yellow arrow).

Finalize models superposition
Click on "ucs 1" (red and yellow arrows) for each model. Then select "constrain" (second picture red arrow), press UCS X axis in both models (second picture yellow arrows) and "apply" (blue arrow). Repeat this process to insert Y and Z coordinates.

Save superposition
After completing superposition by inserting "Z" UCS coordinate (red arrows) click on "ok" ( yellow arrow) and save overlapped model.

Superposed models analysis
To move the model click on the middle of the mouse button and drag model using the positioning cube (red circle)

Calibrate the software for tooth movement analysis
Click on : "tools" (black arrow) and then on "document settings" (red arrow). After that, click on "units"(second picture black arrow). choose Choose "millimeters" and "degrees "(black circles) and click on "apply" ( third picture black arrow).

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Step by Step process to analyze tooth movement in the superimposed model

Buccal-lingual translation (x-axis)
Select T0 model (red arrow) by making T1 invisible. For that, click on T1 model (black arrow) and select and disable "visibility" (red circle). Then click on T0 model (red arrow), "work points"(second picture red circle).
After that, choose a point on the vestibular cuspid tip of first molar (black circle). Repeat the process in T1 model. Use the positioning cube to position the model in order to facilitate the marking of points.

Select the points on T0 (black circle) and T1 models (yellow. circle)
Click on "Tools" (black ring) and then on measure"( red ring).Select both points (red arrows) . Click on " read delta result" on x axis (yellow arrow).

Measure the distance between points:
Souza RXS, Souza GAS, Colares JP, Ianni TMS, Magalhães CS, Guerrero-Vargas JA, Montalvany-Antonucci CC, Macari S -A new way of analyzing tooth movement using universal coordinate system geometry single point superposition in a 3D model if you have difficulty measuring this movement, select T0 model (red arrow), click on the left button and select "transparent " (black arrow) make the measurement using the same steps described above.

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Step by Step process to analyze tooth movement in the superimposed model

Vertical changes: Intrusion or extrusion ( Z -axis )
Click on "tool", (red arrow) then on "measure" (yellow arrow). Select a poin in the incisal edge in the middle of the incisor. After that ,observe the result in: "delta z (blue arrow)". Select initial model (yellow arrow), then click on "work axis"(red arrow).Do not change de position of the model during measure (red arrow of the second picture). Select a point in the mesial and in the distal parte of the incisal edge (white circles). Click on "return" (yellow arrow of the second picture). Repeat the same process with the final model.

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Step by Step process to analyze tooth movement in the superimposed model

Measuring rotation angle
Click on measure (red arrow), select work 1 and 2 (yellow arrows). Then, observe measure result in: "angle"(blue arrow).